w
w
ap
eP
m
e
tr
.X
w
om
.c
s
er
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
9709/61
MATHEMATICS
Paper 6 Probability & Statistics 1 (S1)
October/November 2011
1 hour 15 minutes
*8893649739*
Additional Materials:
Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
JC11 11_9709_61/RP
© UCLES 2011
[Turn over
2
1
When a butternut squash seed is sown the probability that it will germinate is 0.86, independently of
any other seeds. A market gardener sows 250 of these seeds. Use a suitable approximation to find
the probability that more than 210 germinate.
[5]
2
The values, x, in a particular set of data are summarised by
Σ(x − 25)2 = 3762.
Σ(x − 25) = 133,
The mean, x, is 28.325.
3
4
(i) Find the standard deviation of x.
[4]
(ii) Find Σ x2 .
[2]
A team of 4 is to be randomly chosen from 3 boys and 5 girls. The random variable X is the number
of girls in the team.
(i) Draw up a probability distribution table for X .
[4]
(ii) Given that E(X ) = 52 , calculate Var(X ).
[2]
The marks of the pupils in a certain class in a History examination are as follows.
28
33
55
38
42
39
27
48
51
37
57
49
33
The marks of the pupils in a Physics examination are summarised as follows.
Lower quartile: 28, Median: 39, Upper quartile: 67.
The lowest mark was 17 and the highest mark was 74.
(i) Draw box-and-whisker plots in a single diagram on graph paper to illustrate the marks for History
and Physics.
[5]
(ii) State one difference, which can be seen from the diagram, between the marks for History and
Physics.
[1]
5
The weights of letters posted by a certain business are normally distributed with mean 20 g. It is
found that the weights of 94% of the letters are within 12 g of the mean.
(i) Find the standard deviation of the weights of the letters.
[3]
(ii) Find the probability that a randomly chosen letter weighs more than 13 g.
[3]
(iii) Find the probability that at least 2 of a random sample of 7 letters have weights which are more
than 12 g above the mean.
[3]
© UCLES 2011
9709/61/O/N/11
3
6
(a) Find the number of different ways in which the 12 letters of the word STRAWBERRIES can be
arranged
(b)
(i) if there are no restrictions,
[2]
(ii) if the 4 vowels A, E, E, I must all be together.
[3]
(i) 4 astronauts are chosen from a certain number of candidates. If order of choosing is not
taken into account, the number of ways the astronauts can be chosen is 3876. How many
ways are there if order of choosing is taken into account?
[2]
(ii) 4 astronauts are chosen to go on a mission. Each of these astronauts can take 3 personal
possessions with him. How many different ways can these 12 possessions be arranged in a
row if each astronaut’s possessions are kept together?
[2]
7
Bag A contains 4 balls numbered 2, 4, 5, 8. Bag B contains 5 balls numbered 1, 3, 6, 8, 8. Bag C
contains 7 balls numbered 2, 7, 8, 8, 8, 8, 9. One ball is selected at random from each bag.
(i) Find the probability that exactly two of the selected balls have the same number.
[5]
(ii) Given that exactly two of the selected balls have the same number, find the probability that they
are both numbered 2.
[2]
(iii) Event X is ‘exactly two of the selected balls have the same number’. Event Y is ‘the ball selected
from bag A has number 2’. Showing your working, determine whether events X and Y are
independent or not.
[2]
© UCLES 2011
9709/61/O/N/11
4
BLANK PAGE
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/61/O/N/11